Data Sufficiency

If the total weight of d equally weighted objects is 40 pounds, how much does each individual object weigh?

(1) If the weight of each object was 25% greater, then the total weight would have been 10 pounds greater.
(2) If the weight of each object was of pound less, the total weight would have been 7.5 pounds less.


(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Not sure bc I havent done the numbers...just written down the equations...but I think is D

Update
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I have done the numbers now...I will go with B :)

I am a tad confused by the question the 2nd statement says "If the weight of each object was of pound less, the total weight would have been 7.5 pounds less."

But if we remove 1 pound from each object then the total weight should reduce by the number of objects i.e. "d", so according to this statement d = 7.5, how can there be 7.5 objects ?.

I have a feeling there is something wrong with the question.

cris wrote:Not sure bc I havent done the numbers...just written down the equations...but I think is D

Update
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I have done the numbers now...I will go with B

Yah... statement 1 just multiplies both sides of the equation by 25%, so doesn't help us at all.

(i.e. we go from dx=40 to 1.25(dx) = 1.25(40))

Statement (2) should be sufficient, but as Gabriel pointed out there's some missing information. "Was of pound less" should be "was one half pound less", or something, so d ends up an integer.

Stuart,

Can you take sample values for d and explain?
(1) If the weight of each object was 25% greater, then the total weight would have been 10 pounds greater.

I think i'm missing something... Thanks!

Suyog wrote:Stuart,

Can you take sample values for d and explain?
(1) If the weight of each object was 25% greater, then the total weight would have been 10 pounds greater.

I think i'm missing something... Thanks!

Sure.. the original total weight is 40.

Let's say we started with 4 10lb objects.

Using statement (1), we would now have 4 12.5lb objects. Well, 4*12.5 = 50. 40 + 10 = 50. So, the individual weight could be 10lbs each.

However, let's say we started with 40 1lb objects. After the increase, we'd have 40 1.25lb objects. 40*1.25 = 50 and, again, 40 + 10 = 50. So, the individual weight could be 1lb each.

In fact, ANY number you pick will work. If we let x be the weight of each object, then the original equation is:

dx = 40

Once we build in statement (1), we get:

d (1.25x) = 40 + 10

which we can rewrite as:

1.25(d)(x) = 40 + (.25)40

and

1.25(d)(x) = 1.25(40)

finally, if we divide both sides by 1.25 we simply get:

dx = 40, which is our original equation.

In other words, statement (1) gives us absolutely no information that we didn't already have. Accordingly, we can elminate choices (A), (D) and even (C), since there's no way that (1) is going to be part of a "together" solution.

Absolutely!

Thanks a ton... i got what i was looking for... thanks!